As depicted in Fig. 1, we consider an IRS-assisted WPCN, which is composed of an HAP, an IRS, and \(K\)  wireless-powered IoT devices. It is assumed that the IRS is equipped with \(N\)  reflecting elements and the HAP and IoT devices are all equipped with a single antenna. In particular, the HAP with constant power supply (e.g., power grid) coordinates the DL WPT and UL WIT to and from the IoT devices with the assistance of the IRS. For the ease of practical implementation, the HAP and all devices are assumed to operate over the same frequency band, with the total available transmission time denoted by \(T_{\max }\) .
Specifically, the typical “harvest and then transmit” protocol is adopted for the WPCN [1]}, [2]} where the IoT devices first harvest energy from the signal emitted by the HAP in the DL and then use the harvested energy to transmit their own information to the HAP in the UL. For notation convenience, the UL and DL channel reciprocity is assumed for all the channels and they follow the quasi-static flat-fading model. In other words, the channel coefficients remain constant during each transmission block, but can vary from one to another. This also facilitates the DL channel state information (CSI) acquisition based on the UL training. In practice, since the IRS is supposed to be implemented with low cost and low energy consumption, its computational capability is usually limited, which may not be able to afford the computational task for periodically executing the algorithm. As such, the HAP is assumed to be in charge of executing the algorithm and then feedback its optimized phase-shift vectors to the IRS for setting the reflection over time.
